1. Developments on an entirely different track sug-
gest that economists have never abandoned the hope
of proving that utility is after all cardinally measurable.
A remarkably elegant scheme for determining a cardi-
nal scale for utility was developed by Frank P. Ramsey
(1926) and, independently, by O. Morgenstern and John
von Neumann (1944). The scheme follows Bernoulli's
idea in reverse. Bernoulli determined the stake of the
gambler from the knowledge of the gambler's utility
function. The authors just mentioned proposed to de-
termine the utility function of an individual with the
aid of the odds which that individual would be just
willing to accept. They reasoned that if an individual
is just willing to pay five dollars for a lottery ticket
that gives him one chance in two of winning twelve
dollars, we can infer that for that individual the utility
of the additional seven dollars is equal to the utility
of the five dollars that he may lose. By experimenting
with various gambling propositions, we may thus de-
termine step by step how great is the utility of the
individual's n-th dollar in comparison with all his other
dollars. This is tantamount to constructing a utility
scale which, like that of temperature, is completely
determined once the origin and the unit of measure-
ment are chosen arbitrarily.
The idea was received with enthusiasm as well as
with strong reservations. Some authorities on the sub-
ject of utility openly doubted their ability to construct
a cardinal scale even for their own utility. Various
suggestions have been made as to what piece of the
theoretical apparatus may be at fault. Most probably,
the culprit is the assumption that an individual may
be perfectly indifferent between a dollar in hand and
the probable prospect of winning ten dollars. Indeed,
this assumption overlooks the fact that risk adds a new
and irreducible dimension to man's choice (Georgescu-
Roegen, 1954a).
Whatever the fault, the operational feasibility of the
project has never moved beyond the paper-and-pencil
stage and Ramsey's new vision of a psychogalvanom-
eter had no better fate than Edgeworth's hedonimeter.
